thesis

222 Détection de coïncidences dans les neurones bruités
a b
Voltage (mV)
c
Number of synapses p
maximum
Jitter σ j (ms)
maximum
Time (ms) Time (ms)
d e
Number of synapses p
α=0.5
Voltage (mV)
Synchrony rate λ c (Hz)
Output firing rate (Hz)
Coincidence sensitivity Sp
Number of synapses p
Effective number
of synapses αp
Normalized maximum
τ m
Jitter = 3 ms
Synchrony rate λ c (Hz)
Synaptic reliability α
Jitter σ j (ms)
Figure 8.11 – Effect of spike jitter and synaptic failure on coincidence sensitivity.
a. When random jitter is introduced in input spikes, the sum of coincident PSPs has a smaller
maximum, which is determined (on average) by the amount of jitter. b. This maximum
(numerically calculated for many coincident bi-exponential PSPs) decreases with the standard
deviation of the jitter, reaching 50% of its maximum value when the jitter is comparable to
the membrane time constant. c. As a result, neuron models are sensitive to coincidences when
the jitter is smaller than the membrane time constant, not when it is larger (left ; τN=15 ms,
σN =4 mV, w=0.5 mV). For a jitter of 3 ms and a membrane time constant τm=5 ms, the effect
of sparse synchrony on output firing rate is qualitatively similar to the effect obtained with
zero-lag synchrony (0 ms jitter, Figure 8.10). d. If synapses transmit presynaptic spikes with
probability α = 50% (i.e., failure probability is 50%), the effect of sparse synchrony is still qualitatively
unchanged. e. In this case, the impact on output firing rate is essentially determined
by the effective number of synchronous synapses in each event, seen from the postsynaptic side,
which is on average αp (vertical axis), and does not depend otherwise on synaptic transmission
probability α (horizontal axis).
(dashed line). In our theoretical model, coincidence sensitivity is determined by
the peak size of combined PSPs, therefore we expect neurons to be sensitive to
coincidences when the temporal jitter is smaller than τm. This is confirmed by
numerical simulations (Figure 8.11c) : coincidence sensitivity Sp quickly increases
with the number of input spikes when σj < τm (left ; τm = 5 ms here), and introducing
a 3 ms temporal jitter does not significantly change the impact of sparsely
Output firing rate (Hz)
Output firing rate (Hz)